Talk:Character theory

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[edit] No context

In the first line, articles says "of the representation given above". Alas, no representation is given. Is it on purpose ? I'll try to write one when I have time. user michaelmestre

Yes, the text of this page was cut and pasted rather poorly from group representation. The context for the statement can be found there. -- Fropuff 16:37, 2004 Dec 2 (UTC)

[edit] Expanding the article

Some suggestions for where to go next - the completeness of the article could be improved by including material on:

  1. Definition of the kernel of a character.
  2. Lifted characters.
  3. Restriction of a character to a subgroup.
  4. The permutation character.
  5. Linear vs. non-linear characters.
  6. Irreducibility of characters.
  7. Linear characters are the lifts of irreducible characters of normal subgroups.
  8. Irreducible characters as a basis for the vector space of class functions (i.e. complex-valued functions which are constant on conjugacy classes of the group).
  9. The connections between characters and algebraic integers, in particular, the roots of unity.

--Michael Stone 00:23, 20 May 2005 (UTC)

Sounds good to me. Even a few sentences on each would be great; and even full articles if/when a lot can be said. linas 04:51, 20 May 2005 (UTC)

[edit] Notation problem in orthogonality relation

In the paragraph that reads

The orthogonality relation for columns is as follows:

For g, h \in G the sum \sum_{\chi_i} \chi_i(g) \overline{\chi_i(h)} = \begin{cases}\left | C_G(g) \right |, & \mbox{ if } g, h \mbox{ are conjugate } \\ 0 & \mbox{ otherwise.}\end{cases}

where the sum is over all of the irreducible characters χi of G the symbol group C_G(g) looks suspicious. I dare not edit, however, not sure of what was intended. 212.194.88.242 20:21, 16 January 2006 (UTC) Bossavit, CNRS.

Right, the symbol C_G(g) was not defined - it means the size of the conjugacy class. And there is a factor 1/|G| missing. And the orthogonality of rows was not actually stated. I've fixed these now. Paul Matthews 09:27, 21 November 2006 (UTC)

[edit] More expansion

(It would be good to have:)

  1. A more extensive list of the character tables of important groups, such as the symmetric and alternating groups. —Preceding unsigned comment added by 131.111.233.70 (talk) 20:36, 25 February 2008 (UTC)